An analytical model describing the hydrogen gas evolution under natural convection in an electrolyzer cell is developed. Main purpose of the model is to investigate the electrolyte conductivity through the cell under various conditions. Cell conductivity is calculated from a parallel resistor approximation depending on the gas phase distribution. The results are supported by applying a two-phase numerical model which shows good agreement with the analytical approach. The model can prove useful to optimize design factors of an electrolyzer cell for future use in that it provides clear tendencies for electrolyte conductivity from combinations of pressure, current density and electrolyte width among others.